Ardern's partner Clarke Gayford shared a photo of Sheeran reading a pregnancy book with him.
"It takes a village (and a pop star) to raise a child," Gayford said on Twitter.
Sheeran's second show of three at Mt Smart Stadium in Auckland is tonight before he heads south for another three shows in Dunedin on March 29, 31, and April 1.
Meeting with the PM wasn't the only visit he had made to prominent Kiwis. On Friday the 27-year-old chart-topping singer-songwriter also met Black Caps captain Kane Williamson.
"It was fantastic to meet him, a humble guy who enjoys his cricket. It was cool for him to come along today and watch a little bit," said Williamson, who is a part-time guitarist.
Fellow New Zealand players Trent Boult and Matt Henry also chatted to Sheeran.
The team gave Sheeran a Black Caps shirt.